Toehold-mediated strand displacement (TMSD) has been used extensively for molecular sensing and computing in DNA-based molecular circuits. As these circuits grow in complexity, sequence similarity between components can lead to cross-talk, causing leak, altered kinetics, or even circuit failure. For small non-biological circuits, such unwanted interactions can be designed against. In environments containing a huge number of sequences, taking all possible interactions into account becomes infeasible. Therefore, a general understanding of the impact of sequence backgrounds on TMSD reactions is of great interest. Here, we investigate the impact of random DNA sequences on TMSD circuits. We begin by studying individual interfering strands and use the obtained data to build machine learning models that estimate kinetics. We then investigate the influence of pools of random strands and find that the kinetics are determined by only a small subpopulation of strongly interacting strands. Consequently, their behavior can be mimicked by a small collection of such strands. The equilibration of the circuit with the background sequences strongly influences this behavior, leading to up to 1 order of magnitude difference in reaction speed. Finally, we compare two established and one novel technique that speed up TMSD reactions in random sequence pools: a three-letter alphabet, protection of toeholds by intramolecular secondary structure, or by an additional blocking strand. While all of these techniques were useful, only the latter can be used without sequence constraints. We expect that our insights will be useful for the construction of TMSD circuits that are robust to molecular noise.